This is great! Thanks for posting this. I'm going to have to definitely read through it more carefully later.

Also, this reminds of a tutorial that covered PID controllers. There were very good, animated JavaScript diagrams and plots that showed individually why each of the P, I, and D were needed in such a control system with the animations supporting the argument. I have tried finding it before, but I can't find it. It was posted on Hacker News. Does anyone know of one like this?